shown in Fig.1, this technique HGA, GA plus MD, is applied to the search for the structural ground state configuration of a Palladium cluster constitued by 147.
New parallel hybrid Genetic Algorithm based on Molecular Dynamics approach for energy minimization of atomistic systems M.Celino (1), P.Palazzari (1), N.Pucello (2), M.Rosati (3), V.Rosato (2) (1)
ENEA, HPCN Project, C.P. 2400 - 00100 Roma A.D. (Italy) ENEA, Divisione Nuovi Materiali, C.P. 2400 - 00100 Roma A.D. (Italy) (3) CASPUR, Università “La Sapienza” di Roma, P.le A.Moro, 00185 Roma (Italy) (2)
Abstract. A hybrid genetic algorithm (HGA) for the optimization of the ground-state structure of a metallic atomic cluster has been implemented on a MIMDSIMD parallel platform. The concept of building block (BB) is generalized to cover this real-coded optimization problem. On the basis of some reasonings on the dependence of the convergence of Genetic Algorithms (GAs) from BBs, an hybrid genetic algorithm (HGA) is proposed to solve the minimization problem. All the elements of each new population are optimized through a Molecular Dynamics algorithm: the aim of MD is to create ever better BBs and, consequently, to improve the convergence of GAs. HGA has been implemented on a MIMDSIMD platform based on the massively parallel processing supercomputer Quadrics/APE100 which offers a peak performance of 25.6 Gflops; we obtained a sustained computational power greater than 10 Gflops.
due to implicit parallelism and depends on their ability to recombine building blocks (BB) to generate ever “better” solutions [Gol 89]. These characteristics of GAs are lost when we are dealing with real coded GAs, i.e. when the soluction is not considered as a string of literal characters but is represented by a sequence of real numbers. In such a case the classical notion of BB is no more significant.
Fig. 1 : Starting (liquid Pd atomic cluster) and final (obtained through the application of the Hybrid GA) configurations.
1. Introduction A genetic algorithm (GA) [Raw 91] has been recently successfully applied to determine the lowest energy configuration of a Carbon cluster of atoms [Dea 95]. In the present study that algorithm is modified and improved by introducing a further optimization phase which transforms each element of the population through a Molecular Dynamics (MD) algorithm. As shown in Fig.1, this technique HGA, GA plus MD, is applied to the search for the structural ground state configuration of a Palladium cluster constitued by 147 atoms (Pd147). Furthermore the HGA has been implemented on a hybrid MIMD-SIMD platform recently assembled at the ENEA Casaccia Research Centre in Rome, Italy [ENE 96].
2. Generalization of the building block concept It is well known that GAs find near optimal solutions by processing a population of strings through the classical genetic operators : selection, crossover and mutation. Their very good behavior is probably
In this work we want to minimize the potential energy of an atomic cluster constituted by 147 Palladium atoms, so each cluster can be represented by a string with 3*147 real numbers (the cartesian coordinates of each atom), i.e. a configuration is represented by the real string siÎÂ147*3. Even if a lot of work has been developed referring to such real optimization problems (evolution strategies, see for example [Bäc 96]), we found useful to refer to the classical theory of GAs after generalizing the concept of BB. In [Col 95] the concept of schema and BB were formally introduced: we will instaure a parallelism between the notion of schema and of subcluster, then we will define a BB in our real-coded optimization problem. A BB is defined to be a schema H with low order (o(H)
